Finite Group Databasebeta

← C127×#19076 #44582749

Subgroups — C127×#19076 #44582749

Order 32512.

1000 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3548C211yesmaximal, characteristic
2C127×#3165C211yesmaximal, characteristic, complemented
3C127×#3152C211yesmaximal, characteristic, complemented
4C127×#3141C211yesmaximal, characteristic, complemented
5C127×#1661C218yesmaximal, complemented
6C127×#1526C211yesmaximal, characteristic, complemented
7C127×#1525C211yesmaximal, characteristic, complemented
8C127×#1525C211yesmaximal, characteristic, complemented
9C2×#137×C127—22no—
10#562×C127C2214yes—
11#554×C127—21no—
12#554×C127—21no—
13#550×C127—21no—
14#550×C127—21no—
15#547×C127—21no—
16#547×C127—21no—
17#540×C127—22no—
18#537×C127—22no—
19#537×C127—22no—
20#533×C127C2211yescharacteristic
21#532×C127C2211yescharacteristic
22#532×C127C2211yescharacteristic
23C2×C4⋊Q8×C127C2211yescharacteristic
24#501×C127C2214yes—
25#500×C127—21no—
26#498×C127—21no—
27#497×C127C2214yes—
28#494×C127—21no—
29#492×C127—21no—
30#489×C127C2214yes—
31#487×C127—21no—
32#486×C127—21no—
33#428×C127—22no—
34#417×C127—22no—
35C4×M16×C127C2211yescharacteristic
36C4×M16×C127C2211yescharacteristic
37C4×M16×C127C2211yescharacteristic
38#330×C127C2214yes—
39#329×C127C2214yes—
40#329×C127C2214yes—
41C2×#41×C127—22no—
42C2×#41×C127—22no—
43C2×#41×C127D412yes—
44C2×#41×C127D412yes—
45C22×Q8×C127—21no—
46#137×C127—48no—
47C2×Q16×C127—24no—
48C2×SD16×C127—24no—
49C2×M16×C127—21no—
50C2×M16×C127—21no—
51C2×M16×C127—21no—
52C4⋊Q8×C127—21no—
53C4⋊Q8×C127—21no—
54C4⋊Q8×C127—21no—
55C4⋊Q8×C127D411yescharacteristic
56C4⋊Q8×C127D411yescharacteristic
57C4⋊Q8×C127D411yescharacteristic
58C4⋊Q8×C127D411yescharacteristic
59C4⋊Q8×C127C2312yes—
60#127×C127—22no—
61#127×C127D411yescharacteristic
62#127×C127D411yescharacteristic
63#125×C127—22no—
64#125×C127C2312yes—
65#124×C127C2312yes—
66#124×C127C2312yes—
67#123×C127—24no—
68#123×C127—24no—
69C22⋊Q8×C127—22no—
70C22⋊Q8×C127—22no—
71C22⋊Q8×C127—24no—
72C22⋊Q8×C127—24no—
73C22⋊Q8×C127—21no—
74C22⋊Q8×C127—21no—
75#121×C127—24no—
76#121×C127—24no—
77#121×C127—22no—
78#121×C127—22no—
79#121×C127—24no—
80#121×C127—24no—
81#121×C127—21no—
82#121×C127—21no—
83#121×C127—21no—
84#121×C127—21no—
85C4×Q8×C127—21no—
86C4×Q8×C127—21no—
87C4×D4×C127—22no—
88C4×D4×C127—22no—
89C4×D4×C127—21no—
90C4×D4×C127—21no—
91C4×D4×C127—21no—
92C4×D4×C127—21no—
93#117×C127D412yes—
94C2×C4⋊C4×C127—22no—
95C2×C4⋊C4×C127—22no—
96C2×C4⋊C4×C127—21no—
97C2×C4⋊C4×C127—21no—
98C2×C42×C127C2311yescharacteristic
99#107×C127—24no—
100#106×C127—24no—
101#103×C127—24no—
102#102×C127—24no—
103#97×C127C2312yes—
104#97×C127C2312yes—
105#97×C127C2312yes—
106C4×C8×C127—21no—
107C4×C8×C127—21no—
108C4×C8×C127—21no—
109#41×C127—44no—
110#41×C127—44no—
111#41×C127—84no—
112#41×C127—84no—
113C2×Q8×C127—21no—
114C2×Q8×C127—21no—
115C2×Q8×C127—22no—
116C2×Q8×C127—44no—
117C2×Q8×C127—41no—
118C2×Q8×C127C2×D412yes—
119C2×Q8×C127C2×D412yes—
120C2×D4×C127—24no—
121C2×D4×C127—24no—
122C2×D4×C127—22no—
123C2×D4×C127—22no—
124C2×D4×C127—21no—
125C2×D4×C127—21no—
126C2×D4×C127—21no—
127C2×D4×C127—21no—
128C2×D4×C127C2×D412yes—
129C2×D4×C127C2×D412yes—
130C22×C4×C127—24no—
131C22×C4×C127—24no—
132C22×C4×C127—22no—
133C22×C4×C127—22no—
134C22×C4×C127—41no—
135C22×C4×C127C2×D411yescharacteristic
136C22×C4×C127C2×D411yescharacteristic
137C22×C4×C127C2×D411yescharacteristic
138Q16×C127—48no—
139SD16×C127—48no—
140M16×C127—24no—
141M16×C127—24no—
142M16×C127—42no—
143C2×C8×C127—22no—
144C2×C8×C127—22no—
145C2×C8×C127—22no—
146C4⋊C4×C127—24no—
147C4⋊C4×C127—24no—
148C4⋊C4×C127—21no—
149C4⋊C4×C127—21no—
150C4⋊C4×C127—21no—
151C4⋊C4×C127—21no—
152C4⋊C4×C127—21no—
153C4⋊C4×C127—21no—
154C4⋊C4×C127—22no—
155C4⋊C4×C127—22no—
156C4⋊C4×C127—22no—
157C4⋊C4×C127—22no—
158C4⋊C4×C127—41no—
159C4⋊C4×C127—41no—
160C4⋊C4×C127C2×D412yes—
161C4⋊C4×C127C2×D412yes—
162C22⋊C4×C127—24no—
163C22⋊C4×C127—24no—
164C22⋊C4×C127—22no—
165C22⋊C4×C127—22no—
166C22⋊C4×C127—22no—
167C22⋊C4×C127—22no—
168C22⋊C4×C127—22no—
169C42×C127—22no—
170C42×C127C2×D411yescharacteristic
171C42×C127C2×D411yescharacteristic
172C42×C127C2×D411yescharacteristic
173C42×C127C2411yescharacteristic
174C23×C127—22no—
175C23×C127—22no—
176C23×C127#12011yescharacteristic
177Q8×C127—42no—
178Q8×C127—42no—
179Q8×C127—44no—
180Q8×C127—42no—
181Q8×C127—42no—
182Q8×C127—82no—
183D4×C127—42no—
184D4×C127—42no—
185D4×C127—42no—
186D4×C127—42no—
187D4×C127—42no—
188D4×C127—42no—
189D4×C127—82no—
190D4×C127—82no—
191D4×C127—84no—
192D4×C127—84no—
193C2×C4×C127—22no—
194C2×C4×C127—22no—
195C2×C4×C127—22no—
196C2×C4×C127—22no—
197C2×C4×C127—22no—
198C2×C4×C127—22no—
199C2×C4×C127—22no—
200C2×C4×C127—44no—
201C2×C4×C127—44no—
202C2×C4×C127—42no—
203C2×C4×C127—84no—
204C2×C4×C127—84no—
205C2×C4×C127—82no—
206C2×C4×C127#12011yescharacteristic
207C2×C4×C127#12011yescharacteristic
208C2×C4×C127#12011yescharacteristic
209C2×C4×C127C22×D411yescharacteristic
210C2×C4×C127C22×D411yescharacteristic
211C2×C4×C127C22×D411yescharacteristic
212C8×C127—24no—
213C8×C127—24no—
214C8×C127—42no—
215C22×C127—21no—
216C22×C127—21no—
217C22×C127—21no—
218C22×C127—42no—
219C22×C127—42no—
220C22×C127—42no—
221C22×C127—42no—
222C22×C127—42no—
223C22×C127—42no—
224C22×C127C2×#12011yescharacteristic
225C4×C127—21no—
226C4×C127—21no—
227C4×C127—21no—
228C4×C127—42no—
229C4×C127—42no—
230C4×C127—42no—
231C4×C127—42no—
232C4×C127—82no—
233C4×C127#45312yes—
234C4×C127#45512yes—
235C4×C127#45612yes—
236#19076C12711yesmaximal, characteristic, direct product factor, Sylow
237C2×C127—41no—
238C2×C127—82no—
239C2×C127—82no—
240C2×C127C2×#45311yescharacteristic
241C2×C127C2×#45511yescharacteristic
242C2×C127C2×#45611yescharacteristic
243#3548C2×C12711yescharacteristic
244#3165C2×C12711yescharacteristic, complemented
245#3152C2×C12711yescharacteristic, complemented
246#3141C2×C12711yescharacteristic, complemented
247#1661C2×C12718yescomplemented
248#1526C2×C12711yescharacteristic, complemented
249#1525C2×C12711yescharacteristic, complemented
250#1525C2×C12711yescharacteristic, complemented
251C127#1907611yescharacteristic, direct product factor, Sylow
252C2×#137—22no—
253#562C22×C12714yes—
254#554—21no—
255#554—21no—
256#550—21no—
257#550—21no—
258#547—21no—
259#547—21no—
260#540—22no—
261#537—22no—
262#537—22no—
263#533C22×C12711yescharacteristic
264#532C22×C12711yescharacteristic
265#532C22×C12711yescharacteristic
266C2×C4⋊Q8C22×C12711yescharacteristic
267#501C22×C12714yes—
268#500—21no—
269#498—21no—
270#497C22×C12714yes—
271#494—21no—
272#492—21no—
273#489C22×C12714yes—
274#487—21no—
275#486—21no—
276#428—22no—
277#417—22no—
278C4×M16C22×C12711yescharacteristic
279C4×M16C22×C12711yescharacteristic
280C4×M16C22×C12711yescharacteristic
281#330C22×C12714yes—
282#329C22×C12714yes—
283#329C22×C12714yes—
284C2×#41—22no—
285C2×#41—22no—
286C2×#41D4×C12712yes—
287C2×#41D4×C12712yes—
288C22×Q8—21no—
289#137—48no—
290C2×Q16—24no—
291C2×SD16—24no—
292C2×M16—21no—
293C2×M16—21no—
294C2×M16—21no—
295C4⋊Q8—21no—
296C4⋊Q8—21no—
297C4⋊Q8—21no—
298C4⋊Q8D4×C12711yescharacteristic
299C4⋊Q8D4×C12711yescharacteristic
300C4⋊Q8D4×C12711yescharacteristic
301C4⋊Q8D4×C12711yescharacteristic
302C4⋊Q8C23×C12712yes—
303#127—22no—
304#127D4×C12711yescharacteristic
305#127D4×C12711yescharacteristic
306#125—22no—
307#125C23×C12712yes—
308#124C23×C12712yes—
309#124C23×C12712yes—
310#123—24no—
311#123—24no—
312C22⋊Q8—22no—
313C22⋊Q8—22no—
314C22⋊Q8—24no—
315C22⋊Q8—24no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318#121—24no—
319#121—24no—
320#121—22no—
321#121—22no—
322#121—24no—
323#121—24no—
324#121—21no—
325#121—21no—
326#121—21no—
327#121—21no—
328C4×Q8—21no—
329C4×Q8—21no—
330C4×D4—22no—
331C4×D4—22no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—21no—
336#117D4×C12712yes—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C42C23×C12711yescharacteristic
342#107—24no—
343#106—24no—
344#103—24no—
345#102—24no—
346#97C23×C12712yes—
347#97C23×C12712yes—
348#97C23×C12712yes—
349C4×C8—21no—
350C4×C8—21no—
351C4×C8—21no—
352#41—44no—
353#41—44no—
354#41—84no—
355#41—84no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—22no—
359C2×Q8—44no—
360C2×Q8—41no—
361C2×Q8C2×D4×C12712yes—
362C2×Q8C2×D4×C12712yes—
363C2×D4—24no—
364C2×D4—24no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4C2×D4×C12712yes—
372C2×D4C2×D4×C12712yes—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—41no—
378C22×C4C2×D4×C12711yescharacteristic
379C22×C4C2×D4×C12711yescharacteristic
380C22×C4C2×D4×C12711yescharacteristic
381Q16—48no—
382SD16—48no—
383M16—24no—
384M16—24no—
385M16—42no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—22no—
389C4⋊C4—24no—
390C4⋊C4—24no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4C2×D4×C12712yes—
404C4⋊C4C2×D4×C12712yes—
405C22⋊C4—24no—
406C22⋊C4—24no—
407C22⋊C4—22no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C42—22no—
413C42C2×D4×C12711yescharacteristic
414C42C2×D4×C12711yescharacteristic
415C42C2×D4×C12711yescharacteristic
416C42C24×C12711yescharacteristic
417C23—22no—
418C23—22no—
419C23#120×C12711yescharacteristic
420Q8—42no—
421Q8—42no—
422Q8—44no—
423Q8—42no—
424Q8—42no—
425Q8—82no—
426D4—42no—
427D4—42no—
428D4—42no—
429D4—42no—
430D4—42no—
431D4—42no—
432D4—82no—
433D4—82no—
434D4—84no—
435D4—84no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—42no—
446C2×C4—84no—
447C2×C4—84no—
448C2×C4—82no—
449C2×C4#120×C12711yescharacteristic
450C2×C4#120×C12711yescharacteristic
451C2×C4#120×C12711yescharacteristic
452C2×C4C22×D4×C12711yescharacteristic
453C2×C4C22×D4×C12711yescharacteristic
454C2×C4C22×D4×C12711yescharacteristic
455C8—24no—
456C8—24no—
457C8—42no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—42no—
462C22—42no—
463C22—42no—
464C22—42no—
465C22—42no—
466C22—42no—
467C22C2×#120×C12711yescharacteristic
468C4—21no—
469C4—21no—
470C4—21no—
471C4—42no—
472C4—42no—
473C4—42no—
474C4—42no—
475C4—82no—
476C4#453×C12712yes—
477C4#455×C12712yes—
478C4#456×C12712yes—
479C2—41no—
480C2—82no—
481C2—82no—
482C2C2×#453×C12711yescharacteristic
483C2C2×#455×C12711yescharacteristic
484C2C2×#456×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC42C24×C127
prime radicalC127×#3548C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C127×#3165C2semidirect
3. C127×#3152C2semidirect
4. C127×#3141C2semidirect
5. C127×#1661C2semidirect
6. C127×#1526C2semidirect
7. C127×#1525C2semidirect
8. C127×#1525C2semidirect
236. #19076C127direct (N × H)
244. #3165C2×C127semidirect
245. #3152C2×C127semidirect
246. #3141C2×C127semidirect
247. #1661C2×C127semidirect
248. #1526C2×C127semidirect
249. #1525C2×C127semidirect
250. #1525C2×C127semidirect
251. C127#19076direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C127×#35482
C127×#31652
C127×#31522
C127×#31412
C127×#16612
C127×#15262
C127×#15252
#19076127